http://www-math.mit.edu/18.013A/tools/tools04.html
(not yet in Math Tools)
You can use the pull-down functions or you can enter functions by typing. I
asked the students to experiment as they wish on the pull-down functions, but
be sure to try on x^3, x^4, and x^5. Assignment: Of all functions with their
general shapes, what's special about the derivatives of these? Write up what are
the key visual properties of the derivatives of each and draw another candidate
for the derivative of each. (We'd examined the graph of y = x^2 in class and
noticed that it had the amazing property of having y' a straight line and that
other vaguely "parabolic" curves needn't have that property—they'll see that
y=x^4 is another such.)

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.